function data_sim = generate_data(model,settings)
%Modified by Viet Hoang Dinh

% Function for generating simulated data
    % Use a general ABCDEF representation of the encompassing model (DFM, DSGE or others):
        % state transition:  s_t = A * s_{t-1} + B * \epsilon_t
        % measurement eq:    y_t = C * s_{t-1} + D * \epsilon_t + e^*_t
        % measurement error: e_t = E * e_{t-1} + F * \omega_t

        % where e_t = (e^*_t', e^*_{t-1}', ...)'. Warning: e^*_t corresponds to v_t in our paper
        %       \epsilon_t are the structural shocks.
        %       \omega_t are innovations in measurement errors. Warning: \omega_t corresponds to \xi_t in our paper
        %       y_t are observables. Warning: correspond to X_t in our paper
    
    % Warning: shock_weight' * \epsilon_t corresponds to true shock \epsilon_{1t} in our paper
    
    % external IV: z_t = \rho * z_{t-1} + \alpha * (shock_weight' * \epsilon_t) + \nu_t

% unpack settings

T      = settings.simul.T;
T_burn = settings.simul.T_burn;

A = model.ABCD.A;
B = model.ABCD.B;
C = model.ABCD.C;
D = model.ABCD.D;
E = model.ABCD.E;
F = model.ABCD.F;

n_s   = model.n_s;
n_eps = model.n_eps;
n_y   = model.n_y;
n_w   = model.n_w;
n_e   = model.n_e;


%IV setting
rho = 0.1;
alpha = 1;
sigma_v = 0.1;


shock_weight = settings.est.shock_weight;

% draw shocks

data_eps = randn(T_burn+T,n_eps);
data_w   = randn(T_burn+T,n_w);


% simulate states & measurement error

s = zeros(n_s,1);
e = zeros(n_e,1);
data_s = NaN(T_burn + T, n_s);
data_e = NaN(T_burn + T, n_e);
for t = 1:(T_burn + T)
    s = A * s + B * data_eps(t,:)';
    data_s(t,:) = s';
    e = E * e + F * data_w(t,:)';
    data_e(t,:) = e';
end

% simulate observables

data_y = NaN(T, n_y);
for t = 1:T
    data_y(t,:) = C * data_s(T_burn + (t-1),:)' + D * data_eps(T_burn + t,:)' + data_e(T_burn + t, 1:n_y)';
end

% simulate IV
z=zeros(T+T_burn,1);
for it=1:T+T_burn
    if it==1
        z(it,:)=alpha*data_eps(it,:)*shock_weight+sigma_v*randn(1,1);
    elseif it>1
        z(it,:)=rho*z(it-1,:)+alpha*data_eps(it,:)*shock_weight+sigma_v*randn(1,1);
    end
end
data_z = z(T_burn+1:end);



% collect results and shift timing

data_sim.data_y     = data_y;
data_sim.data_shock = data_eps((T_burn+1):(T_burn+T), :) * shock_weight;
data_sim.data_z     = data_z;

end